SOLUTION: The vertex angle of an isosceles triangle is 80%. find the area if the measure of the congruent sides are 14in. round to the nearest tenth.

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Question 1035431: The vertex angle of an isosceles triangle is 80%. find the area if the measure of the congruent sides are 14in. round to the nearest tenth.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
You must mean to say "degrees" and not "percent". This would seem to perfectly fit the use of Law of Cosines.

14%5E2%2B14%5E2-2%2A14%2A14%2Acos%2880%29=b%5E2 and b is for base size of the triangle.

Next, you want the height. Your base angles each are 50 degree. The height segment forms two right triangles, each with a leg b%2F2.

Area will be %281%2F2%29%28b%2F2%29%2Ah; and you would now already have calculated b. You might just use Pythagorean Theorem formula, h%5E2%2B%28%281%2F2%29b%29%5E2=14%5E2.

Answer by ikleyn(52914) About Me  (Show Source):
You can put this solution on YOUR website!
.
The vertex angle of an isosceles triangle is 80°. find the area if the measure of the congruent sides are 14 in. Round to the nearest tenth.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

S = %281%2F2%29b%2Ah.

%281%2F2%29%2Ab = 14*sin(40°)    ( 40° = 80%5Eo%2F2 )

h = 14%2Acos%2840%5Eo%29.

------->   S = 14*sin(40°)*14*cos(40°) = %281%2F2%29%2A14%5E2%2Asin%2880%5E0%29 = 98*sin(80°) square inches.